The Vreg cycles the alternator power strength to keep the battery voltage in an acceptable range. If it gets too high the alternatore backs off. If there is more load than the alternator is currently making then the battery voltage goes down a little and the vreg responds by jacking up the alternator power output. These changes make the voltage level go up and down by some amount. Incandescent bulbs react slower to voltage changes than LEDs.
I'd guess your pulsing is from Vreg cycling.
Depending on the response time of the multimeter, and the frequency of the pulsing, you might be able to see the voltage change on the meter display.
You might also see what the voltage variance is on the tail light power leads, by putting the meter into an AC volts range. This would then measure the ripple riding on the DC voltage.
You might also check the electrolyte level of the battery. If it is low, the battery has less ability to smooth out voltage due to load variations and alternator cycling. Finally, if you have a smaller battery than stock, the reduced impedance can also add to line voltage variations, like a standard battery with low electrolyte.
At any rate, the investigation begins with voltage level monitoring.